Elimination of quotients in various localisations of premodels into models
| Autor: | Tuyéras, Rémy |
|---|---|
| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Mathematics, 5(3), 37, (2017) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.3390/math5030037 |
| Popis: | The contribution of this article is quadruple. It (1) unifies various schemes of premodels/models including situations such as presheaves/sheaves, sheaves/flabby sheaves, prespectra/$\Omega$-spectra, simplicial topological spaces/(complete) Segal spaces, pre-localised rings/localised rings, functors in categories/strong stacks and, to some extent, functors from a limit sketch to a model category versus the homotopical models for the limit sketch; (2) provides a general construction from the premodels to the models; (3) proposes technics that allows one to assess the nature of the universal properties associated with this construction; (4) shows that the obtained localisation admits a particular presentation, which organises the structural and relational information into bundles of data. This presentation is obtained via a process called an elimination of quotients and its aim is to facilitate the handling of the relational information appearing in the construction of higher dimensional objects such as weak $(\omega,n)$-categories, weak $\omega$-groupoids and higher moduli stacks. Comment: The text is the same as in v6; this version contains corrections to the published MDPI paper, the main reason for this change is that the diagram of Proposition 3.1 was meant to be a 3 dimensional diagram (while only the front face appeared in the published paper). The wording of some sentences and the diagram of Example 6.42 are changed accordingly. A typo in the table of Ex. 6.42 is corrected |
| Databáze: | arXiv |
| Externí odkaz: |
|